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C₂×#7628 #160738

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(4,7,8,9)(12,16)(13,14)(17,18)(19,20,21,24,22,23,25,26);(3,4)(5,9)(6,8)(7,10)(11,12)(13,16)(14,18)(15,17);(11,13,15,14)(12,16,17,18)(20,23)(24,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 67934);